Problem 14 Simplify. $$\left(-4 y^{3}\rig... [FREE SOLUTION]

Chapter 9: Problem 14

Simplify. $$\left(-4 y^{3}\right)(2 y)$$

Short Answer

Expert verified

The simplified form of the expression $-4y^{3} * 2y$ is $ -8y^{4}$.

Step by step solution

Identify the Terms

In the given expression, there are two terms $-4y^{3}$ and $2y$. Both of these terms have to be multiplied to simplify the expression.

Apply multiplication rule

When multiplying two terms that have the same base (in this case, 'y'), the exponents should be added together. So when $-4y^{3}$ is multiplied by $2y$, it becomes $ -4 * 2 * y^{(3+1)}$. The multiplication of coefficients (-4 and 2) equals -8 and the sum of the exponents (3+1) equals 4. So the simplified expression becomes $ -8y^{4}$.

Simplify

The end result $ -8y^{4}$ is the simplified version of the given expression $-4y^{3} * 2y$. This cannot be simplified any further as there are no like terms to merge.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Exponents

Exponents play a crucial role in mathematical expressions, especially when dealing with polynomials. An exponent indicates how many times a number, known as the base, is multiplied by itself. For example, in the expression $ y^3 $, $ y $ is the base and 3 is the exponent, meaning $ y $ is multiplied by itself three times: $ y \cdot y \cdot y $.

When handling expressions with exponents, especially during multiplication, you must remember the golden rule: add the exponents if the bases are the same. For instance, when multiplying $ y^3 $ by $ y^1 $, their exponents are added to become $ y^{3+1} = y^4 $. This makes it convenient to simplify polynomial expressions.

Multiplication

Multiplication is the process of calculating the total of one number multiplied by another. In terms of algebra, this can involve more than just numbers; it can also involve variables and coefficients. When multiplying terms like $-4y^3$ and $2y$, you need to do two things: multiply the coefficients and manage the exponents.

Here's a simple guide to follow:

Multiply the coefficients: $-4$ times $2$ equals $-8$.
Multiply the variables: Add the exponents of $y^3$ and $y$ (which is $y^1$), resulting in $y^{3+1} = y^4$.

By following these steps, you will find the product of the initial terms, which becomes $-8y^4$.

Simplification

Simplification is about reducing an expression to its simplest form, making it easier to understand and work with. In the context of our original exercise, simplification involves utilizing the rules of exponents and multiplication to combine terms. The given expression $-4y^3$ and $2y$ is simplified to get $-8y^4 $.

Here鈥檚 how it's done:

First, multiply the coefficients $-4$ and $2$ to get $-8$.
Next, use the law of exponents: Add the exponents of $y^3$ and $y^1$ to get $y^4$.

The outcome is the simplest form $-8y^4$, where there are no further like terms or further reductions possible. Simplification is essential in solving algebraic expressions efficiently.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify. $$\left(-4 y^{3}\right)(2 y)$$

Short Answer

Step by step solution

Identify the Terms

Apply multiplication rule

Simplify

Key Concepts

Exponents

Multiplication

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Geometry

Calculus

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.